Bayesian estimation of an AR(1) process with exponential white noise

The object of this paper is a Bayesian analysis of the autoregressive model X t  = ρX t−1 + Y t where 0 < ρ < 1 and Y t are independent random variables with an exponential distribution of parameter θ. Our study generalizes some results obtained by Turkmann (1990). Our analysis is based on a more general non-informative prior which allows us to improve the estimators of ρ and θ.